The human eyes cannot easily focus on two separate targets at the same time. However the two eyeballs can rotate in opposite directions when the target approaches or leaves. The two eyes have their own cooperative movements called conjugate and vergence eye movements. Since the classifications of eye movement patterns in physiology are based on the phenomena of eyeball rotations, it is difficult to use in mathematical analysis. This paper first redefines the concepts of binocular movements from the view point of system control engineering, and then discuss the relationship of conjugate and vergence eye movements using a mathematical model based on the human neural pathways of the binocular motor system. Here we suggest that in fact fusional vergence is saccade, accommodative vergence ([1], [20]) is smooth pursuit, flow induced vergence ([1]) is OKR, and the vergence occurred by head movement is a family of VOR. At last, we show an application of the cooperative binocular motor system on a mobile robot. Since the binocular system exhibits several characteristics specific to human-eye movements, such as both eyes moves in tandem with the same target point in the central area, the robot can use the rotational angles of the two eyes to detect the gazing target position, and let the mobile robot keep a constant distance from the target.